It is known that various types of devices have been used heretofore for the adjustment of rails transversely of their longitudinal axes, and the reader may refer to the West German Patent 2409510/A in the name of Talke, or either one of the two East German Patents 116482/A and 114110/A both in the name of Noke. However the most desirable features in such a sleeper arrangement, as also in other civil engineering applications, include the provision of considerable strength in the adjustment means, easy positioning of the rail fasteners, and easy transverse movement of the rails.